Units

The crew wished to convert the 7,682 liters of fuel to its equivalent went in kilograms. In order to do so the crew applied an incorrect conversion factor (1 liter of fuel weighs 1.77 kg.) Actually, 1 liter of fuel weighs 0.803 pounds, but the crew used an improper weight.

The crew inaccurately calculated ed the weight of the fuel onboard the aircraft to be 13,597 kilograms. The erroneous calculation is shown below.

Next, the crew went about determining the weight of fuel that would need to be transferred to the fuel tanks. They found this to be 8,703 kilograms, as shown in the differencing operation below

Finally, the volume of fuel in liters that needed to be transferred to the fuel tanks before departure for Edmundton was calculated. Once again, the erroroneous conversion factor was used as shown below

As consequence of these steps, the ground crew transferred 4,916 liters of jet fuel into the fuel tanks. Both the air and ground crews incorrectly believed that this volume of jet fuel (4,916 liters) would be sufficient to insure a safe arrival in Edmundton. Unfortunately, the sequence of calculations contained errors and the aircraft was forced to glide to a safe landing well short of its desired target.

Let us now examine the steps of calculation that should have been performed and that would have enabled a safe landing of the aircraft in Edmundton. We first determine the correct weight of fuel that remained in the fuel tanks upon the aircraft’s arrival in Ottawa. Here, we use the proper conversion information. That is one liter of jet fuel weighs 0.803 kilograms.

So only 6,169 kilograms of fuel remained in the fuel tank when the aircraft landed in Ottawa. The next step involves the determination of how much fuel needed to be transferred to the fuel tank in order to accomplish the flight to Edmundton. This is properly computed by differencing the weight of the fuel needed to accomplish the flight to Edmundton and the weight of the fuel remaining in the fuel tanks.

Thus a quantity of jet fuel weighing 16,131 needed to be transferred by the ground crew into the fuel tanks in order to insure the safe arrival of the aircraft in Edmundton. This weight of fuel (kilograms) can be converted to a volume (liters) as follows

Now this conversion factor can be used to determine the number of liters of fuel that should have been transferred to the fuel tanks.

We conclude that 20,088 liters of fuel needed to be transferred to the fuel tank to successfully complete the leg of the flight from Ottawa to Edmundton. This represents approximately 4 times as many liters of fuel as was incorrectly calculated by the air and ground crew in 1983. The inadequacy in the provisioning of fuel resulted in the “Gimli Glider” having to perform an emergency landing well short of its desired arrival location. Due to some skillful piloting of the aircraft, no one onboard was seriously injured.

Summary

This chapter has attempted to illustrate the level of importance that engineering students should assign to the topic of units. In addition, a procedure that allows for the conversion of a quantity expressed in one unit to another unit has been presented. This method is quite simple in that all it requires is that one multiply the quantity expressed in the original unit to be multiplied by a fractional form that is equal to the integer 1. A process for correctly determining the proper fractional form is presented also.

Engineering students should view mastering the topic of units as an importance step in their formal education as an engineer. They should keep in mind that virtually all problems in engineering courses will involve solutions that include units.

Events surrounding the NASA Mars Climate Orbiter and the “Gimli Glider” show how seemingly small mistakes involving units and conversion factors can cause failures to complex systems.

Exercises

1. Convert 1,052,832 feet to miles, meters, kilometers, and yards. Express each answer using 3 significant digits of accuracy.
2. How many millimeters, centimeters and meters are in 62.8 inches? Use 1 inch = 2.54 centimeters. Express each answer using 3 significant digits of accuracy.
3. Find the range of temperature in degrees Fahrenheit (⁰F) for the following range of temperatures in degrees centigrade/Celsius (⁰C): -15⁰C to +25⁰C .
4. “Normal” body temperature is said to be 98.6⁰F + 0.6⁰F. Convert these values to Celsius and give the answer in terms of minimum and maximum values.
5. If a computer file is 8.2 gigabytes and the effective transfer rate is 41 megabits per second, how long does it take to transfer the file from one location to another? Assume that 1 byte = 8 bits.
6. Homeostasis is the condition of keeping our bodies alive by regulating its internal temperature and maintaining a stable environment. Approximately 2,000 calories per day are required to maintain the human body. It is known that 1 calorie is equivalent to 4.184 joules and that one watt is equivalent to one joule per second. Determine the number of watts that are equivalent to 2,000 calories/day.